What Holds the Longitudinal Arch Up??

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We take certain things in life for granted. We expect our automobiles to run smoothly, expect our computers to not lose important data, and expect electricity to be supplied to our homes 100% of the time. In fact, the normal function of these machines and services lulls us into complacency regardiing our consideration of how these machines and services actually work so well most of the time.

However, when the car quits running, when the computer crashes and when the lights go out, we all start to be much more concerned about these problems and begin to be much more interested in how these modern day machines and services actually work. Human nature?....I suppose.

Likewise, when it comes to the human foot, we, as podiatrists and foot-health professionals, tend to take for granted that a foot should normally have a certain arch height or shape that is neither too high or too low under weightbearing loads. However, when the longitudinal arch of the foot isn't normally shaped, we have all sorts of ideas and theories as to why the arch is either abnormally flat or abnormally high. We don't seem to have near as much interest in what causes a foot to have a normal longitudinal arch as when it doesn't have a normal height or shape of longitudinal arch.

With this in mind, my question is this:

When an individual has a normal longitudinal arch height during weightbearing activities, what are the mechanical factors that has allowed the foot to maintain this arch height under the weightbearing loads of the body and not have an abnormally flat or abnormally high arch shape??

I invite all to respond to this question....please don't be shy.

 

Dear Kevin

If one considers the MLA as a 2D arch or a triangular truss structure the same basic principles apply to each. The force vectors of applied forces must be contained within the structure otherwise there is a tendency for failure by collapse from shear or bending or strain.

So for the arch to be stable without any other supporting structures it must be of the catenery type and stiff enough to resist compression strain but this is not the case of the foot arch.

The triangular truss or the non-catenary arch must be tied along its base by a rigid structure in the form of a tie or rigidly fixed at each end. This will stop the collapse of the structure as the supporting load-bearing ends are forced away from each other.

If we assume, as in the foot, that the load is applied to the arch or truss in a direction oblique to vertical then there are vectors of that force acting thru the structure that will tend to shear, compress, torsion or tension the material. The material itself must then be stiff enough to bear these forces.

If the structure is segmented as in a stone built arch bridge or the bones of the foot the joint of each segment must fixed in such a way as to prevent shear or separation of the joint that will lead to collapse of the structure. In the case of the bridge often this is the job of the cement and the compressional forces that increase internal moments between segments plus buttresses are added to take these force vectors that are directed outwith the structure of the arch. In the foot this is the job of ligaments and muscles.

The foot is not a fixed and rigid structure therefore as the load and shape of the structure changes so must the forces that keep the foot arch/truss stable. This is the job of the muscles.

If we consider the foot as a triangular truss where the calcaneous is fixed and the met heads are a roller then as vertical loads are applied the roller can move away from the fixed heel. The tie, that stabilises the triangle, is the plantar fascia plus ligaments and musculature that exert force in the same plane such as the short and long extensors and spring ligament. The plantar Fascia and ligaments have a fixed stiffness (for the purposes of this explanation).

The applied load will tend to strain the plantar fascia, increasing the distance between mets and heel, and so lower the height of the truss. Providing the PF etc is stiff enough the truss will remain stable at a certain height depending on the load. However the applied load will also cause moments about the structure and particularly about its segments which will tend to bend and separate. The individual joints have ligaments that resist bending but may not be sufficient to resist collapse. So there are secondary forces applied by muscles such as anterior tib and posterior tib. These seem to pull the arch or truss height up but since they are attached to the shank any increase in force to pull up the truss height or resist bending will result in an equal and opposite increase in load. Therefore it is more likely that these muscles increase the compressional forces between segment joints and thereby increase resisting joint moments that increase the stiffness of the structure and resist collapse. Note that the Calcaneous has no muscular attachments that tend to resist bending since the structure of the bone itself is massive enough to be very stiff and resist collapse from bending or torsional stress. Unlike the columns that are long, slender and segmented levers that require augmentation to remain stiff to applied load.

In summary the 2D arch or truss to remain stable must be able to resist tension forces in the tie (PF), compressional and shear forces and bending moments of the supports (bones), shear and torsion forces at the segment joints (ligaments and joint forces).
To enable dynamic flexibility in the structure forces resisting the variable load (which is variable in magnitude and direction) need to be variable in the same way (i.e. Muscles) to keep the required morphology and resist collapse.
When all these systems are in place and operating at optimal level the arch will be stable and normal thru gait. If one of these systems fail then increased load will be applied to other structures and eventually collapse will result. This is the difference between a normal (former) and pathological (latter) foot arch system.

How does that sound to you Kevin?

 

Dave

Totally agree with your explanation but I would like, if possible, to expand on Kevin's original question.
As well as purely mechanical factors, what other factors are essential?

Some of our answers may be educated guess work but I don't think it can all be mechanical in the pure sense that Dave has outlined.
E.g mechanoreceptor feedback control of intrinsic and extrinsic stabilising muscle function - see post fatigue changes in foot function. Do the changes in interosseous muscle function change significantly enough to allow us to model the arch differently e.g as a more fluid body?

Hope this makes sense.

Cheers

Phil

 

Phil

I understand what you are saying but the basic mechanical model must be understood before we can consider the muscle controling mechanism.

The rigid body model is valid but the flexible body model is more accurate to decribe the exact location of forces and moments and stress and strain.
Even if when we know the minutia of muscle action and tissue deformation can our orthoses be sophisticated enough to make changes at that level.

Dave

 

Dave

Why does the mechanical model need to proceed the physiological model?
The bodies ability to alter the forces that it is experiencing, either proactively or reactively, are powerful enough to override GRF, gravity etc.
E.g put a person on a FFO and measure pressure at day 1 and week 8. You will see massive differences. This may be due to proprioception, mechanical feedback or other.
I think that is one of the reasons for us not totally understanding the impact of FFO's. If it was purley mechanical then the resultant forces of the ORF should be precitable - they arn't.

Don't get me wrong, I use the mechanical model as a starting point and without it I would not be able to treat my patients, however the arch is a significant structure that never seems to respond predictably.

Phil (Playing Devils Advocate?)

 

Dave, Phil and Colleagues:

Dave: Very nice reply. Probably one of your most well-written and most thorough responses yet.

But, to ask my question again, what are the specific mechanics involved in making a longitudinal arch normal in height versus making a low or high longitudinal arch?? You did answer my question the way I thought you would, from an engineering perspective. However, when a podiatrist, who is not an engineer, looks at a normally shaped arch, what are the mechanical and neuromuscular (thanks Phil) factors that they should consider that is either causing or perpetuating this height or shape of their longitudinal arch?

 

Phil

The physics of the mechanical model are constant, you are talking about a system of control. You can't understand and build a control system without knowing what it is you need to control and how to control it and the limitations of the model.

No the bodies muscular system cannot override gravity or GRF only change the way they interact with the body.

I presume you mean pressure pattern differences, I don't know about that, what do you mean by massive? do have any referrences? Pressure mat and insole systems have a very large error range of around 15-25%.
But even taking what you say as true the mechanics will hold true. The pressure changes don't happen by magic there is a mechanical reason. A certain muscle was activated, which changed the force and moment balance thru the foot. We do not have Finite element models that can accurately predict the changes but they will follow mechanical principles, guaranteed.
How those changes are initiated by a control system is a different consideration and we need to know how, if and what those contols systems are.

We don't, I agree, but the orthoses may push buttons which activates a control system that initiates a mechanical change.

The changes can only be mechanical. The control systems are perhaps unkown and unpredictable but the mechanics are well known, but not always easily measurable and therefore not easily predictable.



All the best, Dave

 

Phil:

I think that to the clinician your viewpoint is very important. However, from the engineering perspective that Dave has given us, he is also correct in pointing out that even though changes in muscle activity seen with or without orthoses may occur due to central nervous system (CNS) control, these changes are indeed ultimately responsible for the mechanical function of the foot and as such may be modelled using a mechanical system, with a central controller (i.e. CNS) modifying the muscle activity of the foot and lower extremity.

Passive mechanical factors (i.e. mechanical factors not under CNS control) and active mechanical factors (i.e. mechanical factors under CNS control) of the foot and lower extremity should be recognized as two distinct types of mechanical factors that ultimately affect longitudinal arch height during weightbearing activities. This type of categorization should help bridge the gap in communication between biomechanists and clinicians.

It is important to understand that passive mechanical factors would include the viscoelastic mechanical characteristics of the bones, hyaline cartilage, ligaments and tendons and their relative geometry to each other during loading conditions, irrespective of muscle control. A fresh-frozen cadaver foot that has been brought up to normal temperature would be a good example of how a foot woud respond mechanically if only passive mechanical factors were present.

However, active mechanical factors are under CNS control and may involve changes in the recruitment pattern, contractile activity and temporal patterns of foot and lower extremity muscle activity. Examples of various types of CNS controls include conscious volitional control, and alterations in muscle activity due to changes in proprioceptive input, due to pain avoidance, due to balance maintenance, due to injury avoidance and due to generalized stimulation or depression of the CNS.

Hopefully this helps.

 

Dave

Good points but lets carry on the discussion.

The Physics of the mechanical model may be constant but due to the body being inconsistent - fatigue, de-hydration etc - is this model good enough to be used?

You are right re the bodies ability to alter forces - should have said react to external forces resulting in these forces being negated or changed significantly enough to not be relavant to the modelling of the arch.

My experience, and that of a few others I have been exposed to, show that pressure distribution, COP and COM can be different to such a level that a pronating foot acts as a supinating foot when 1st wearing insoles. This can confuse the whole orthotic prescription process. In some patients you only get an accurate estimation of ORF 8 weeks later when they are totally used to them.
I think the terms used by Kevin - active and passice mechanical factors are ideal to explain what we know and don't know about the arch modelling.

I always use a mechanical based approach to patient assessment - partially because it is the most straight foward approach and partially due to it being the most medico-legally defensible position (Sad but true that I feel that I always cover my back due to litigation etc).
However my hands on assessment of QOM, ROM and AROM are so reliant on non-mechanical assessment parameters, the role of the active mechaniocal factors are just as important to the whole treatment approach.

All the best

Phil

 

Phil

I pretty much agree with the sentiment of your post but I have some problems with the concept with trying to use unknown or little understood control systems to determins changes in the orthotic prescription.

I know people do have antalgic strategies and proprioceptive strategies and balance strategies but do I understand enough about them to use in my prescription. Well No, I don't, barring balance perhaps.

Are control system or active mechanical methods contrary to mechanical methods.

EG I want to reduce or stop pressure bearing on the plantar heel of my patient. Should I use a U pad or doughnut or should I place a tack / drawing pin in the heel cup. One is passive mechanical the other is an active method
ie the muscles are activated by the brain to stop anticipated pain of standing on a tack. I don't think the patient would like walking on tip toe all day though and niether will his calf muscles or the met heads. Does this mean that if I want a supinated foot position I should make an uncomfortable or painful arch profile in my orthoses. If I do will the muscular effort of supinating the foot cause other pathology. The nice thing about the passive mechanical theory is that it tends to reduces stress in the tissues that one requires it to without increasing stress in others. (ideally)


Its all a bit of science and a bit of art and a bit of magic (experience) at the end of the day. Don't you think Phil?

Cheers Dave

 

Dave

I like a little bit of hocus pocus with my biomechanics, so orthotic prescribing fits well.
I like your analogy of using pain avoidance mechanisms to change foot function - the sadist in me likes the black and white effect it gives and the masochist likes the hassle I'll get from the patient.
However to bring this specifically on to orthoses, I now feel that gross prescriptions such as heel raises are the only really predictable 'passive mechanism' inducing changes that I am confident with. I like to be able to accelerate or decelerate the patients COP to get symptom relief - that would be my apporach to your heel pain patient.
When it comes to frontal plane control, I am now much more in favour of adapting footwear as the point of application is outside the body and the resultant moments larger and more direct. I hope to put footwear prescribing to the forefront of my clinical work as its fits my mechanical approach far more comfortably and the client group I am currently treating (The at risk foot)
When it comes to the 3 arch's of the foot, I prefer to try and facilitate their normal function and let the foot sort itself out via its autosupportive mechanisms - along the lines of your description of what supports the MLA. Where these are not working, then I use my orthoses to do the job.

I think we are both very alike as we don't like not knowing why somethings works - you because of your mechanical background and me because of stroppy nature (I hate not knowing).

Cheers

Phil

 

Kevin and Dave have said pretty much what I want to say, but this is a subject dear to me so I will say some of the same things a little differently.

In modeling the foot you can call it an arch, beam and/or truss. What you call it does not really matter. What matters is that you understand the forces that the arch must withstand. From this understanding you can KNOW some things about the foot.

When the heel is posterior to the ankle joint, body weight and ground reaction force create a force couple that will create a plantar flexion moment on the rearfoot. If the rearfoot is not plantar flexing relative to theforefoot you know there must be some forces creating a dorsiflexion moment on the rearfoot. These forces will be tension in the ligaments, muscles and fascia and compression forces in the bones. What other choices are there for these forces that must exist? This creates a redundant situation where there may be no tension forces in one of those named structures, but there must be tension in at least one of them, otherwise the arch would collapse.

The example you gave about fatigue is something that proves the above. The muscles can provide tension forces. When they fatigue they will provide less tension and the other structures then must have more tension. In this situation the ligaments are more likely to udnergo strain and elongate alowig partial collapse of the arch of the foot.

This model is not that complicated. You just have to look at the sturctures that can provide the forces needed to resist the external forces acting on the foot.

COP and COM location are behaviorally determined. That is why it may change for up to 8 weeks. Change in positoin of these variables are not pure mechanical effects. That said they can still be indicators of improved function.

The reason that I feel that these ideas are so important is that some people will try and use hocus pocus (or voodoo) explanations of why something works. Say you plantar flex the first metatarsal when you cast to make an orthosis. The first ray may be more plantarflexed when the foot is on the orthosis. The cast was taken at a different point in time and has no direct effect on the position of the first ray when it is on top of the orthosis. If the first ray is more plantar flexed on the orthosis you have to explain it by using the existing forces acting on the ray when it stands on the forces.

Knowing these arch modeling concepts will help you make better decisions and better explanations of how orthoses work.

Cheers.

Eric Fuller

 

Thanks for that reply, Eric. I believe you are hitting on the answer to my original question.

Regardless of whether a foot is noted to have a low arch, high arch or a normal arch shape during relaxed bipedal standing, then the same basic mechanical principles apply:

1. Any tendency of ground reaction force to mechanically cause a flattening deformation of the longitudinal arch (i.e. rearfoot plantarflexion and forefoot dorsiflexion) must be met by an internal resistance to this flattening deformation by the structural components of the longitudinal arch, or the arch will flatten further.

2. This internal resistance to flattening deformation of the longitudinal arch may be best expressed as a rearfoot dorsiflexion moment and a forefoot plantarflexion moment.

3. The plantar aponeurosis, plantar arch ligaments, intrinsic muscles, posterior tibial, flexor digitorum longus, flexor hallucis longus and peroneus longus, all work together to produce a rearfoot dorsiflexion moment and a forefoot plantarflexion moment. In this way, these layers of plantar arch structures offer redundant systems to allow the foot to generate sufficient internal resistance to arch flattening moments. Since all of the plantar arch structural components may resist arch flattening simultaneously, we don't have a way to solve how much the plantar fascia, plantar ligaments, plantar intrinsics or extrinsic plantar arch muscles may contribute individually to produce internal resistance to arch flattening. However, we may be able to, with current modelling technology, calculate how much the cumulative effect is of these structures working together to produce internal resistance to arch flattening moments.

Maybe Eric or Dave or someone else can contribute further on this concept of redundancy in the tensile load-bearing structures of the plantar longitudinal arch of the foot.

Now here is how I would answer the question:

The individual with a normal longitudinal arch height possesses this arch height since, during weightbearing loading of their plantar foot, this normal arch shape is that specific geometry of the internal structure of the foot where the rearfoot plantarflexion moments and forefoot dorsiflexion moments from ground reaction force are exactly counterbalanced by the rearfoot dorsiflexion moments and forefoot plantarflexion moments from the effects of the tensile load-bearing structures of the plantar arch of the foot. In other words, a normal longitudinal arch height will be noted to occur in a foot during weightbearing activities only when rotational equilibrium has occurred across the midtarsal-midfoot joints with the osseous components of the foot aligned in a normal arch-shaped geometry.

 

So what should one try to do, when the MLA is accentuated? If clinically relevant, how do we reduce the rearfoot d/f moment and the forefoot p/f moment?

 

Dear Kevin and all

I believe that redundancy may account in some way for the fact that often we see smaller changes in position than we might expect when we fit a foot orthosis.

For instance suppose there are four structures resisting pronation moments 1) Joint forces 2) Ligaments forces 3) Primary muscle force 4) secondary muscle force.

Say this foot requires 400Nm units of supinating moments about the joint to maintain the joint position. Primary muscle contributes 200, joint 50, ligament 125 and secondary muscle 25. The secondary muscle is a primary muscle for another action and the force that it exerts to achieve 25Nm at the joint of interest is also the optimum force required for its primary use and the secondary force is just a useful by product.

Now if for some reason the primary muscle became fatigued or traumatised and was not able to produce 200Nm torque then several things may happen. There could be a positional change and therefore = increased stress on the passive structures which = increased strain in the ligament and /or joint. Or the secondary muscle could increase its work and there may not be a positional change and no increase in stress of the passive structures. I.E. primary muscle 150Nm, Secondary muscle 75Nm, joint 50Nm and ligament 125Nm. Clearly the stress on the secondary muscle has increased by a factor of 200% and it is unlikely that this muscle can maintain this stress without failure in the near future. This may equal pain in the secondary muscle and perhaps some pathology to distal structures. Previously these distal structures only required the force equivalent of 25Nm from the secondary muscle (which is their primary muscle) and therefore they are overloaded or their spatial relationship has changed. So along comes the podiatrist with an FFO. The FFO exerts 50Nm (very clever podiatrist, OH! It must have been me ) and so the brain says Oh! That’s just what was needed and releases 50Nm from the secondary muscle.
Now the balance is Primary muscle 150Nm, secondary muscle 25Nm, joint 50Nm, Ligament 125Nm and FFO 50Nm = 400Nm which is required for that certain joint position, which is the same position as original but augmented by the FFO. The difference is the muscle is not excessively stressed and no pain.

Perhaps redundancy is a little misleading since no muscles or passive structures are redundant in the way that they have no use unless another structure fails. More that they have a primary and secondary function dependent on what is the joint of interest.
When secondary function become primary then there can be pathological changes both proximal and distal to the joint of interest.

How does that sound?

All the best Dave

 

Dave et al

I think this explanation and approach is getting really close to how we can model the arch. I like the idea of modelling the key structures in this way.
The idea of positional muscles suddening becoming mobilising muscles in an attempt to re-instate equilibrium really starts to explain why an orthoses may work like magic - they re-instate the ZOOS.
I think the main issue I have with modelling is that it is not specific to my patient sat in front of me and can only provide guidance and not specific answers e.g. without MRI etc I don't know which structure is not taking its fair share of the load required to maintain an non-pathological state. This may be lazy but is a reality of the clinical environment.
I do like the mechanical approach, though, as it makes a lot more sense than pronation/supination approaches.
Thanks for the maths Dave, I am glad you can do as I can just about follow it, never mind working the whole thing out.

Cheers


Phil

 

Phil

This is the skill of the clinician to take the model and apply it to an individual.
By diagnosing the correct structure that is traumatised and by intimate and detailed knowledge of anatomy can define the direction of forces/stress within the stucture and design the orthoses to apply an optimal opposite force to relieve or reduce the stress within.

I have deliberatly tried to avoid complicated maths since this is something you can't apply to each patient without sophisticated data collection and analysis but the principles can be applied and will work if the clinical skills are good.

It is both a strength and weakness of the bodies biomechanical system that muscles have an oblique pull to the axis of the joint that it tends to rotate.
This means that when a certain muscle is activated to move a joint in a given direction, lets say flexion, then the action of that muscle will also tend to have a secondary action, lets say internal rotation, Now if internal rotation is undesirable for the required action then a second muscle must be activated. The primary action of this muscle is internal rotation but it also abducts. A third muscle is activated to stop abduction but this third muscle has a secondary affect of extension, which is contrary to the initial required action. Therefore the initial muscle that flexes must exert more force and so it goes around.
This makes for a very difficult analysis process when dealing in absolute force and moment balances and you may see that it would be much more convenient if the muscle action worked at right angles to the axis and only caused the primary joint motion EG just flexion. However the weakness of this system would be that if the primary muscle failed how would the joint then move, it would require a redundant backup system, how inefficient would that be in terms of unwanted mass requiring energy to carry around allday. Imagine a 70kg man may have to be 90kg to accomodate a secondary system and then his primary system would be fatigued more easily anyway, so his primary muscles would have to be bigger, more heavy, and so on. So therefore you can see that although inconvenient for biomechanists the former oblique system has a built in redundancy without any structure being truely redundant and all structures being useful at all times to different degrees.

Cheerio for now, Dave (good discussion)

 

If your patient has plantar fasciitis it is specific to your patient. This arch modeling explains why the pathology occurs and how you can treat it. You can make the diagnosis of plantar fasciitis without an MRI. I would agree that there are times where you are not sure of the diagnosis, but you can proceed with the treatment and see if it works without getting addtional diagnostics tests. In some cases the treatment will cost less than the additional tests. The mechanical approach would require you to look at what factors would increase stress on the plantar fascia.


[/QUOTE]
I do like the mechanical approach, though, as it makes a lot more sense than pronation/supination approaches.
Thanks for the maths Dave, I am glad you can do as I can just about follow it, never mind working the whole thing out.
[/QUOTE]


Pronation moments at the subtalar joint and forefoot dorsiflexion moments are resisted by tension in the fascia. So, the mechanical, or tissue stress approach looks at both pronation/supination moments as well as sagittal plane moments. This approach doesn't require math either. All you have to know is what variables are involved and then try to alter the variables. For example if a high pronation moment from ground reactive force is present in your patient with plantar fasciitis then your treatment should be directed at , for example, reducing pronation moment from ground reaction force (e.g. medial heel skive). Or you can reduce sagittal moments or both sagittal and proantion moments. So, the process is make the diagnosis and then model the structure you think is injured and then treat the foot with interventions your model would predict reduce stress on the structure.

Cheers,

Eric Fuller

 

Here is what my computer dictionary says about redundancy:

Redundancy: (electrical engineering) duplication of components: the installation of duplicate electronic or mechanical components or backup systems that are designed to come into use to keep equipment working if their counterparts fail
Microsoft® Encarta® Reference Library 2005. © 1993-2004 Microsoft Corporation. All rights reserved.

The concept of redundancy for describing the functions of the plantar fascia, plantar ligaments and plantar intrinsics would probably only be an appropriate term to use if one is not considering normal function, but rather is considering an injury situation (e.g. when a plantar ligament or plantar fascia experiences a partial tear, an plastic elongation or a total rupture).

However, "primary and secondary function" is also not very good terminology since this concept is totally dependent on one's opinion of what is the most important mechanical function for a structural component of the foot that has multiple mechanical functions. For example, what is the primary and secondary functions of the plantar fascia?? What is the primary and secondary function of the peroneus longus muscle??

Probably a better way of describing how the plantar fascia, plantar ligaments, plantar intrinsics and FDL, FHL, PT and PL all contribute to producing rearfoot dorsiflexion moments and forefoot plantarflexion moments during normal circumstances is to say that all of these structures share tensile loading forces in the plantar arch. In other words, the fact that each of these plantar arch structures work together to prevent arch flattening should be considered to be a load-sharing system.

For example, all of these structures are subjected to some magnitude of tensile loading force during normal weightbearing activities. However, the more tensile load that one structure is subjected to, the less will be the tensile load in another structure, given the same arch geometry and identical magnitude of arch loading forces. All of these structures share the load in most situations. They only replace the load of another structure when that structure fails.

Great discussion!

 

Phil:

You are wrong here. As Eric said, you don't always need to even know which structure is specifically injured (don't need an MRI or diagnostic ultrasound) to get good clinical results. All you need to know, in many cases, is what the abnormal loading force acting on a set of tissues of interest is and then simply find a way to reduce the abnormal load on that tissue so that pain is reduced and more normal gait function if reestablished. This "tissue stress approach" can only be done practically in a clinical situation by using modelling techniques. We can't put force transducers or strain gauges within the tissues of our patients. We must model the forces to direct our clinical therapy.

These models don't need to be exceedingly complex. They can be something as simple as the clinician being able to accurately predict that a foot with plantar fasciitis, where the injury is caused by increased tensile forces within the plantar fascia, may have a lessening of plantar fascial tensile loading forces with decreased Achilles tendon tension or decreased body weight or with a low-Dye strapping placed on their plantar arch. All that is required is that the clinician understand basic force diagrams, basic models of the foot and understand very basic engineering concepts. Eric and I are committed to making certain that the next generation of podiatrists will become better trained in these concepts than we ever were.

 

Kevin

Maybe my interpretation of the original question is different to others but I was assuming that the modelling of the arch was an attempt to produce an exact 'model' of the foot that could explain all forces etc. (The definition I work to is that modelling is a mathematical description of a system)
The reason I have questioned this exact modelling concept is that it is NOT applicable to my patient but its principles are. This may be semantics on my part and again due to my interpretation of the term modelling. (I work with CAD engineering software and the term modelling has a different meaning for me.)
Maybe the term modelling should be renamed 'theoretical modelling' as we cannot get absolute data for every foot. I am not sure?
You use the term modelling techniques and I would agree that they are essential - again I may be being too literal.
Just to re-iterate, I think the original question and all the answers are excellent put again need to be put in context for the clinician. We may be capable of modelling as true biomechanist and taking this infornmation into the clinic but that is where the biomechanics stop and the clinicians ability to use the 'theories' starts.
Hope this makes sense.

Phil

 

Kevin

The term of primary function is not without precedent: ref Musculoskeletal assessment, Joint range of motion and manual muscle strength. Clarkson H M: L.W.W. NY ISBN 0-683-30384-8.
The whole basis of modelling is that one makes certain assumptions that allow the model to be valid. So at the time of analysis or assessment one can assume that a certain muscle has a primary action. Biceps femoris has a primary action of knee flexion but also is a significant external rotator. Whether this external rotation is primary or secondary is subjective and dependent on the position of the knee, the applied load, the primary direction of action required and how the observer defines external rotation of the knee. The Knee is externally rotated as a whole by the muscles that externally rotate the hip eg piriformis, gemellis, obturator the part of biceps femoris in this is very small.
The moments required to flex the knee may be small if the applied load is mainly that action of internal rotation and therefore the moments produced by Biceps Femoris (BF) to externally rotate may be relatively large it could then be argued that this is its primary function at that time. Therefore the analyst may decide to assume that the primary function of BF is external rotation, for that analysis.

However, having said that, it is also common to define the action of a joint in terms of a group of muscles. This group of muscles can have a primary action EG knee flexion, which is the group of muscle consisting of biceps femoris, semi-tendinosus and semi-membranosus. The internal rotation effect of the medial hamstrings (ST and SM) cancels the external rotation effect of BF and the action is pure flexion. This is when the observer is interested primarily in knee flexion. What if the observer is interested in hip adduction then the group is Adductors – Brevis, Magnus and Longus but if the hamstrings are also contracting and as the origin of the medial hamstrings are in the medial ishium then they also have a secondary action of adduction.
So as you imply Kevin, the terms primary and secondary are not a fixed definition for each and every muscle and change in the way described. However I think they are a useful definition when used within the terms defined by the observer and by the assumption for the model at the time of analysis.

Therefore it may be useful for the clinician to decide on which is the primary muscle or primary muscle group for the action of interest. Then assess what are the secondary muscles or structures that may have been or could be conscripted to augment the action in times of fatigue or pathological trauma of the primary set. This may lead to a conclusion about which structure may be excessively stressed, or, if worked in reverse, why a muscle is pathologically affected by a seemingly unconnected change in gait or joint action.

All the best, Dave ( Kevin, you started a really good thread of discussion with your ‘simple’ question)

 

Agree

 

Here is what Benno Nigg said about modelling:

A model is an attempt to represent reality.
(Nigg, B.M.: "Modelling", In Biomechanics of the Musculo-skeletal System, 2nd Edition, (B.M. Nigg and W. Herzog, eds), John Wiley and Sons, New York, 1999, pp. 423-532.)

Models come in all levels of complexity, from simple free body diagrams to finite element models. They only need to be basic for the clinician making decisions as to how to reduce stress on a tissue. Phil, with your interest in biomechanics, you should purchase this book and read, what I consider, this most excellent chapter on modelling that has ever been written within a biomechanics book.

 

Kevin

I have now reset my mind set on modelling and will try and get a copy of Niggs book - I think I have most of his other work so not sure how I missed that one.

Cheers

Phil

 

Kevin replied
Redundancy: (electrical engineering) duplication of components: the installation of duplicate electronic or mechanical components or backup systems that are designed to come into use to keep equipment working if their counterparts fail
Microsoft® Encarta® Reference Library 2005. © 1993-2004 Microsoft Corporation. All rights reserved.

The concept of redundancy for describing the functions of the plantar fascia, plantar ligaments and plantar intrinsics would probably only be an appropriate term to use if one is not considering normal function, but rather is considering an injury situation (e.g. when a plantar ligament or plantar fascia experiences a partial tear, an plastic elongation or a total rupture).


Eric adds:

The definition of redundancy is a little different in mechanical engineering than electrical engineering. My mechanical engineering text defines statically determinent as having the minimum number of structures needed for support. For example a board supported on both ends by a saw horse. Redundancy is where something is statically inderminate, or in other words when there are more structures than the minimum needed to maintain equilibrium. (I'm paraphrasing slightly as I don't have the text in front of me.) A redundant situation would the same board supported by 3 sawhorses.

The arch of the foot is a redundant structure in this sense. There are many structurs that can apply tension to create a moment to prevent arch flattening.

I hope I wasn't to redundant in my writing.

Eric

 

Here's the 3rd edition of the book at www.amazon.com:

http://www.amazon.com/Biomechanics-..._bbs_sr_1/103-2247678-8253439?ie=UTF8&s=books

I have both the 1st and 2nd editions of this book. The section on modelling is somewhat technical but really goes into great detail about the concepts of modelling. You just won't find this information anywhere else in one book! Just wish I didn't feel like I was the only podiatrist that has read this book.

 

Redundancy certainly makes sense to me. Can you find that definition in your textbook for me Eric??

However, I like the idea that the multiple ligamentous and muscular structures within the plantar arch of the foot are a load-sharing system. I think I will start using that term in my lectures, along with redundancy, to help get the message across with more descriptive terminology. Load-sharing is a very good mechanical description of how the plantar arch structures work together to help the foot maintain longitudinal arch height during weightbearing activities. The concept of load-sharing is used in descriptions of mechanical and biological systems already. Here is an interesting paper on the concept of load-sharing in peripheral nerves in diabetic and nondiabetic rats. http://www-personal.umich.edu/~amsastry/publications/JBME2004.pdf

 

Dear Eric

This basically true but is not strictly correct, Static indeterminance in construction / structural engineering is where the principles of static equilibrium are insufficient to determine support reactions AND internal stress distribution in a structure.(Structural an stress analysis: Megson THG,Butterworth Heinman, London ISBN 340 63196 1) Mathematically speaking there are to many unknowns and not enough equations. In this case we need to use some kind of cheat technique like adding a release / break or removing a beam but leaving the structure stable or FEM. The rule of thumb here is M=2J-3 = Number of members = 2 x number of joints or nodes - 3. If M<2j-3 then the structure is unstable if M>2j-3 then the structure is indeterminate.
The Additional beam/s or support/s is/are only considered redundant by the fact that if it was removed the structure would still be stable and statically determinate. EG a triangular truss with an additional support from appex to centre of base is statically indeterminate (try the rule of thumb) since this beam could take all the vertical load applied or none of it or any load value in between. Removing the support leaves a stable and statically determinate triangular truss. This latter truss however will not be potentially as stiff as the former with the support in place.
A similar problem is kinematic indeterminancy and this is where there are to many unknowns but not enough equations to solve the reactions and stresses in a dynamic structure, which in 3D has 6dgs of freedom. Three translational and three rotational.

All the best Dave Smith

 

Kevin, Eric and Phil

I put together this analysis of a model of the hip joint in adduction(attached). I think it shows how muscles can share work for equlibrium and how some set of muscles that might do the same work can be secondary or redundant depending on how you like to think of it.
This is only a valid model analysis when using the assumption that are made.
However that is the nature of modeling when we have many unknows and not the mathematical capacity to deal with them. This still gives a reasonable insight into the probabilities and possibilities of the mechanical interactions in an inherently ambiguos system. I believe this insight can then lead to enhanced clinical evaluation.

PS I have uses the hip instead of the ankle or STJ since it is a much simpler joint to analyse and understand.

Cheers Dave Smith

 

Dave:

Very nicely done. I hope to go over your numbers with a fine tooth comb this weekend but your drawings are very good! I see you have started to master CorelDraw?

Time you started to put your considerable talent into something more widely read and referenced. How about submitting a paper for publication into one of the peer-reviewed podiatry journals for a start?? You are definitely there now! I think that everyone should get to know the Dave Smith we have all grown to respect and enjoy.

 

Dear Kevin

Thank you for your kind words they are much appreciated since it was your influence that took me in this direction.
I am getting there (publishable paper) but time, money and a novel project idea that doesn't require too much of the former is the main problem.

As you will appreciate the maths were only included to show that the numbers on the model were realistic. The important aspect is that it shows that muscles work together in 3 dimensions to achieve equilibrium between internal and external forces and moments. Their obliquness to the axis of interest gives them the ability to do this while at the same time having primary and secondary actions but never true redundancy. The muscles in the model are conveniently placed and their force vectors strategically aligned so that the maths work quite well. In real life (in vivo) they will not be quite so convenient and the analysis would run on and be more complicated. EG +/- Y axis moments would not balance and another set of muscles must be found to do this without upsetting the balance of the first set to much. Or a different assumption about the muscle actions of the first problem must be made.

Oh yes I use corel draw a lot now I have used in all my papers submitted for my MSc. It gives a very professional look. Once again thanks to you for starting me off on it.

All the best Dave Smith